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Time-symmetry in Guillaume de Machaut's "Ma Fin est ma commencement"

Guillaume de Machaut lived from about 1304 to 1377. His three-part song "Ma fin est ma commencement et ma commencement est ma fin" (my end is my beginning, and my beginning is my end) is an example of a crab canon: It is the same forwards and backwards!

The three voices, called the tenor (independent voice), the cantus (the song) and the triplum (third part) contriubute to the overall palindromic shape of the piece. The lowest voice, the tenor is a true palindrome, while the other two voices are the reverse of one another. The graphic below shows a colorful depiction of the three voices, their three minutes condensed to a few inches from left to right. The tenor can be seen in green, while the other two voices in orange and lavender are retrogrades of one another.

(By the way, the word "tenor" meant something different to Machaut than it does to us. It is not a high male voice.)

Several clever people have made videos to show the palindromic nature of the piece.

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